The shocking figures revealed when fouls, penalties and cards are compared.

By Mike

I shall start by making it clear that I’m 99% behind Usama , Walter et al in their referee analyses (well nobody’s perfect) and the article on the Crystal Palace game triggered me into doing a little more research.

In that article, the question was asked, “But still has there ever been a season in the history of Arsenal where we were not awarded a penalty at home???” So I thought I’d check because in all honesty, I’ve been beginning to wonder whether we’ve ever had a damned penalty!! So I just thought I’d point out that we actually didn’t get a home penalty in 2011/12 either, sorry boys!

I’ve only looked back as far as 2002/03 and before we put too much stock by our own apparent misfortune, the Spuds actually went two consecutive seasons (2011/12 and 2012/13) without a home pen.   Maybe it’s just a north south divide in terms of refereeing!

However, given Mike Riley took over before the start of the 2009/10 season it’s interesting to note some anomalies since that date. For example, I have taken a cursory look at the ‘traditional top four’ of Arsenal, Chelsea and the two Manchester clubs in seven seasons Riley has been the Godfather. (I’d like to have done the whole league but gathering facts is incredibly time consuming as others will testify……although very worthwhile as it makes unsubstantiated opinions look very silly sometimes.)

Anyway, between them the four clubs have been awarded 177 penalties in the premiership under Riley.   So by my reckoning, given we’ve constantly been in the top four whilst the others haven’t, if it all evens out we would have got 25% of those i.e. 44.25. In fact it’s actually just 31. That’s far fewer than the second lowest which is Man U at 43 (and in fairness they’ve had a couple of abysmal seasons during the seven seasons in question). Meanwhile, the other two have both had over 50 each……yes that’s 60% more than us.

It gets worse though. I thought I’d have a look at the penalties awarded against the ‘top four’ to see whether that told us anything. Not unnaturally given they do more attacking and less defending you would expect them to concede fewer than they commit.

And so it transpires. A total 96 in fact. That’s an average of 24 each. So (as everything evens itself out in the end) we’ve had just 24…………..sorry, my mistake, we’ve actually had 35. That’s over 50% more than the second highest at just 23. Well that doesn’t seem to all even out in the end so I dug deeper.

Now I’m not a believer in conspiracy theories but I am a believer in conspiracies. And as a team with close to the highest possession stats and best territorial advantages I find it quite inconceivable that the following table for penalties for and against could actually exist unless we’re doing something terribly wrong. So I looked for evidence. The pens for and against though, looked like this.

Club Pens for Pens against Pen. Disparity
Arsenal FC 31 35 – 4
Chelsea 52 23 + 29
Manchester City 51 20 + 31
Manchester United 43 18 + 25

So the others are all getting twice as many for than against but we could not even break through the 50/50 barrier.

But based on my perception of possession etc., how could this be? Perhaps I was wrong.  Well not really the average possession over the seven seasons is pretty even. (There is a slight anomaly with Man U I admit, so I have to guess that the reason that Man U has a relatively low number of penalties to possession ratio is because they’ve barely crossed the half way line since SAF retired!).

So the average possession over 7 seasons is as follows. The opposition have had the ball less against us, so one pointer to the fact that they might be awarded fewer penalties……….

Club Pens for Pens against Pen. Disparity Possession
Arsenal FC 31 35 – 4 56.7%
Chelsea 52 23 + 29 54.6%
Manchester City 51 20 + 31 55.1%
Manchester United 43 18 + 25 55.7%

So next I thought we’d look to see if there’s a correlation between the number of fouls committed and penalties awarded and also fouls conceded and penalties conceded. (Please keep at the back of your mind though that all these fouls and penalties are what the refs actually gave rather than what they could/should have given!)

So, now with the average fouls committed (according to the refs) per game over seven seasons added

Club Pens for Pens against Disparity Possession Fouls
Arsenal FC 31 35 – 4 56.7% 10.5
Chelsea 52 23 + 29 54.6% 11.1
Manchester City 51 20 + 31 55.1% 11.6
Man United 43 18 + 25 55.7% 11.1

So clearly the penalties conceded per foul is way off track. We’ve actually committed fewer fouls than the others (some 300 fewer than Man City in fact).

When we look at that the number of fouls committed for each penalty conceded it looks like this.

Club Pens for Pens against Disparity Possession Fouls Fouls per pen
Arsenal FC 31 35 – 4 56.7% 10.5 79.6
Chelsea 52 23 + 29 54.6% 11.1 128.7
Manchester City 51 20 + 31 55.1% 11.6 153.7
Man United 43 18 + 25 55.7% 11.1 164.5

So basically, under Riley we have conceded about twice as many penalties per foul than either of the Man U clubs even though we are committing far fewer fouls…………….that all evens out in the end then!!!

So what about the bad side of our opponents’ game? How many fouls have been committed against us on average per game (according to the refs)

Club Pens for Pens against Disparity Possession Fouls by Fouls per pen Fouls against
Arsenal FC 31 35 – 4 56.7% 10.5 79.6 11.4
Chelsea 52 23 + 29 54.6% 11.1 128.7 11.8
Man City 51 20 + 31 55.1% 11.6 153.7 10.0
Man Utd 43 18 + 25 55.7% 11.1 164.5 10.7

So clearly the Manchester clubs are fouled far less but still do well on penalties.

So how many times are each team fouled for each penalty they get? Let’s see now, will that even itself out?

Club Pens for Pens against Disparity Possession Fouls by Fouls by per pen Fouls against Fouls against per pen
Arsenal 31 35 – 4 56.7% 10.5 79.6 11.4 97.7
Chelsea 52 23 + 29 54.6% 11.1 128.7 11.8 60.3
Man C 51 20 + 31 55.1% 11.6 153.7 10.0 52.2
Man Utd 43 18 + 25 55.7% 11.1 164.5 10.7 66.2

So yet again we see how difficult it is for us to get penalties whilst those clubs which are being fouled less (whilst actually committing more themselves) are up to 87% more likely to get a penalty. Well that even’s out then….NOT.

So maybe it’s because we put in more tackles per game and consequently there are more opportunities for it to go wrong. So average tackles per game made by each club over the last seven seasons.

Club Pens for Pens against Disparity Possession Fouls by Fouls by per pen Fouls against Fouls against per pen Tackles per game
Arsenal 31 35 – 4 56.7% 10.5 79.6 11.4 97.7 19.7
Chelsea 52 23 + 29 54.6% 11.1 128.7 11.8 60.3 19.6
Man C 51 20 + 31 55.1% 11.6 153.7 10.0 52.2 19.7
Man Utd 43 18 + 25 55.7% 11.1 164.5 10.7 66.2 19.6


So clearly that’s got nothing to do with it. So I wondered whether it maybe about how bad the fouls are? The only indicator I could think of for measuring this was the number of cards received. (Again we must bear in mind the arbitrary nature of cards given e.g. Kos got a red and Costa never even committed a foul at the Bridge earlier in the season!!)

I know there are different ways of calculating the worth of a red card but I’m going to keep it simple and count a yellow as one disciplinary point and a red as two. Hence over the past seven seasons how did the teams do?

Well at the time of writing AFC have played one more game than CFC and MUFC but still we have received less disciplinary points than both those teams. Aha! I hear some dissenters shout…so we’re not as hard done by as is claimed……..I’ll come on to that.

So disciplinary points over seven seasons:

Club Pens for Pens against Disparity Possession Fouls by Fouls by per pen Fouls against Fouls against per pen Tackles per game Discip pts
Arsenal 31 35 – 4 56.7% 10.5 79.6 11.4 97.7 19.7 439
Chelsea 52 23 + 29 54.6% 11.1 128.7 11.8 60.3 19.6 472
Man C 51 20 + 31 55.1% 11.6 153.7 10.0 52.2 19.7 472
Man U 43 18 + 25 55.7% 11.1 164.5 10.7 66.2 19.6 440


So on that basis our fouls are no worse than anybody else’s which suggests they warrant a card (and given we actually seem to get one or two for breathing in the direction of an opponent!!). In fact we are considerably less malicious than two of the other three (and bearing in mind a Man U player is more than likely to just receive a ticking off unless a machete comes into play, I’d suggest we’re better behaved than all of them).

So what about the idea that if we receive fewer cards, we must be receiving reasonable treatment from the refs (assuming they get all their calls right and any mistakes/bias evens out at 50/50……yeah right!).

Well let’s look at how many fouls we committed and how many cards we received (or disciplinary points in this case). Well the number of fouls committed and number of points is as follows.

  • Arsenal 2785 fouls for 439 points
  • Chelsea 2960 fouls for 472 points
  • Man City 3074 fouls for 472 points
  • Man U 2960 fouls for 440 points

I’m sure you can see where this one’s going. Whilst we are committing the fewest number of fouls we are still picking up cards at a faster rate than any of the others. We get a card every 6.3 fouls whilst Man U gets one every 6.7. And whilst this doesn’t seem like much of a difference it still makes little sense (and we have to consider at what point in a game we get those cards too which makes a considerable difference).

Now in conclusion, I will reiterate that I am not a statistician but there are a lot of facts here. (NB for those of you who only deal in opinions, facts are what are needed to give an opinion some credence and will help you to be taken more seriously).

Yet despite the number of facts, I do accept that none of this is conclusive evidence of anything. I would however suggest that having looked at this subject from quite a few different angles, the facts do tend to strongly support the argument that there is a degree of bias against Arsenal by the PIGMOB and that Riley is a Muppet (although the evidence for that was overwhelming before I chipped in).

I’d be hugely interested to debate this with anybody who wants to put the work in to find several facts that would support an opposing view. That could be help the wider debate.

I’ll leave it with you.

Recent Posts

36 Replies to “The shocking figures revealed when fouls, penalties and cards are compared.”

  1. Nice write up Mike now we just need the club to do something about it is getting way out of hand now like PIGMOB I rubbing our faces in it while being backed by the poodits

  2. Mike

    That is brilliantly put together.

    I’ve tried to do similar, but couldn’t do it as well as that, so I’m glad somebody did.

    Now, here’s the alternative,stat-based view…just kidding.

    Hard to imagine what the stats could be to support an alternative view.

  3. Mike — I know you’ve taken a lot of time to crunch the numbers. Unfortunately, in my opinion, any conclusions reached in your exercise above are invalid from a statistical standpoint. Also, a lot of the relationships you use (e.g. a link between possession and the award of penalties) defy logic because penalties are random events.

    Firstly, the average possession for the top-4, over the 7 seasons, according to your numbers is 55.5%. Arsenal is 1.2% points higher at 56.7% and Chelsea 0.9% points lower, with 54.6%. This is actually a very tight range, and could be viewed as statistically insignificant. Now let me ask you, how is possession defined and computed? How precise/accurate is this number? What is the statistical error in this computation? I’ve watched games where the possession stats just doesn’t jive with my own assessment of the game I’ve just watched. This is very different from say a tennis game, where for e.g. the number of shots in a long rally is discussed. This number is very precise, and very few people, if any, can argue over how to compute this.

    Secondly, and assuming the computation of possession stats is indeed rigorously done, shouldn’t you really be looking at possession within the penalty box? Any possession outside the penalty box will not lead to a penalty, so is irrelevant in the case you’re trying to make. (I’m assuming your numbers above are total possession, but correct me if I’m wrong).

    Thirdly, possession in the penalty box doesn’t necessarily lead to a penalty. This is also the case with linking fouls and penalties; not all fouls in the box leads to a penalty, and this is, and always will be, the main point of contention in the game. A penalty award, like a goal, is a random event, and no one (as far as I know) can predict with any certainty the probability of any team being awarded a penalty before the game. And so you’re trying to find correlation to a random event, and this is just not possible. Since it’s a random event, the only thing one can analyse is the event itself; i.e the penalty decision, and related to this, the non-award of a penalty.

    If you really want to show that there is something funny going on, what you should do is start by looking at ALL the penalties for the top-4 teams over the last 7 seasons (for example). For each penalty decision, get an independent judge team of 5 to decide if the penalty award was the correct one. Next, you can look at all cases where a penalty could have been awarded, but was not. How many of these “non-awards” were correct decisions? If you really, really want to be more rigorous with the analysis, it would be better to look at ALL penalties (and non-awards) for ALL teams, over the 7 seasons. An analysis of these numbers would be much more conducive to drawing more logical conclusions.

  4. Mike,

    Well done for both finding and analysing these numbers. I have tried to do something similar this season and gave up due to not finding the raw data.

    As I understand it the freely available possession statistics are normally calculated from the attempted pass numbers. This is indicative of the possession time but isn’t an exact match, it also doesn’t differentiate between the areas of the pitch where the passes were made. A number of defensive passes counts towards overall possession for that team whilst most supporters will register the attacking team as benefitting from that period of play. I agree with you over the need for a far more rigorous analysis of the penalty decisions – it will cost a reasonable sum of money to conduct, a minimum of six people for say 2.5 hours per game, 38 games per team per season times 7 (or more) seasons. Without a wealthy backer that kind of analysis simply isn’t going to happen. The various interests in charge of the game won’t co-operate and will do everything possible to obstruct such an exercise as they all want the status quo to remain. For now all we supporters can do is to keep making pieces of the coffin such as this analysis in the hope that someday it will be possible to nail it all together with the guilty parties inside it.

  5. Mike, a very interesting article and analysis – it certainly illustrates a very alarming trend, one which I would like Riley to try to explain – not that he ever will.

  6. A lot of time and effort there however regarding possession stats it’s almost impossible to find how much of it was actually in the penalty box. We spend a lot of time with the ball but rarely have more than one player in the box itself, most of the time we have it in midfield.

  7. Dojkat

    Don’t know where to start with discussing what you’ve said.

    What you always hope for when you present a case or argument, as Mike painstakingly did, is that anyone who wishes to argue against it will have been attentive to what was said, represent it faithfully and argue directly against that.

    When someone doesn’t, things get messy quickly.

    The big giveaway it went the latter way with your response is ‘Thirdly, possession in the box doesn’t necessarily lead to a penalty’

    That seems to be arguing against what would be an almost impossibly absurd suggestion- that during any game when you have a lot of possession in the box, a penalty will soon to arrive for you.

    Nobody thinks that, surely, (unless it’s a rigged game and you know it) and it is absolutely not what Mike suggested.

    It’s surely a matter of probability : all else being equal, the team with the greater possession in a football match is more likely to be fouled in the opposition penalty box than the opponent is ; this can be slight or overwhelming during a game – (i.e at any moment when you are in the opposition penalty box there is some chance of them conceding a pen and no chance of you conceding a pen, and so in any game where you spend a lot of time in the opposition box and they spend almost no time in yours, the probability of you being fouled in the box is reasonably high and the probability of conceding a pen is low, or during the times they are not in your box, non-existent)- but it is only over longer periods of time that probability should reliably be represented in results. *

    It’s a shame to have to try explain it, testing my reasoning and language abilities as it does, largely because it feels that shouldn’t be necessary.

    Just take probability, in general and in football. Take it, and bloody help me with it someone! Probability, odds, yikes. What are they? What are they in football? We know that bookmakers are very good at setting odds. You can even call them experts at it.

    They deal in the likelihood of something occurring. The game itself could be termed a non-stop stream of random events, a chaos of a kind (one which experts dedicated to studying these things believe is determined by 50% skill, 50% luck), yet they believe they can set figures for the probability of certain outcomes, and they are very good at doing so.

    Why, why is it more likely that Real Madrid will beat Rayo Vallecano than the opposite, or Arsenal Bournemouth, etc? In short, it is because of the ability of those teams. The very same rules govern the likelihood, or should, of Real madrid getting a penalty vs the odds of Rayo getting one; ditto us and Bournemouth. If you doubt this, think about the odds bookmakers would give you for it. Why, why would they believe it much more likely Real get the pen than Rayo? Similarly, why should it be much more likely we get one than Bournemouth do?

    All MIke’s efforts can be seen as an attempt to explore probability in the only way possible. Producing a picture which can be effortlessly read and which, well, does not look right at all.

    What I have said or tried to say seems so obvious to me, so true and obvious and irrefutable, it doesn’t feel like it needs explaining, nor that it could be confused with suggesting a penalty will happen at any time as a result of having more possession than the opposition, or being in their box a lot, etc

    *(Anyone with a great understanding of the Law of Large numbers would be useful here)

  8. Well thought out, it would be incredibly difficult to determine any of this as fact as you alluded to, however with more than 36 Million Fans on Twitter alone, and somewhat mute tones during the proverbial protest during the Norwich game, I think some enhancements to the Forum(s) may be in order.

    It is indeed obvious that bias occurs, democracy is a lie, however masses may effect change, it is entirely about numbers. Imagine, people voted on passages of law, as well as the law makers and the prescriber of law, you would likely have to pool candidates and create a series of publicly available options for legislative change but it would be something much more like a democratic representation of popularised opinion.

    I think that highlighting the bias is difficult, but corruption would leave a financial trail and money often gets the other PIGMOB motivated, they just need to take a few years to realise the world isn’t analogue any more and the Millennium bug was a media creation.

    Individually finding a trail of small pebbles or rather money would likely lead to at least one house made of sweets, that allayed to a likely statistically supported propensity towards bias would likely produce a credible platform from which to suggest that on the balance of probability (the civil law standard) credence could be given to the suggestion of corruption and therefore the implication on any particular team(s). A thorough examination of the evidence in this manner would likely yield evidence which would be appropriate for a criminal investigation.

    It is the Premier Leagues own interest to improve it’s image with huge revenues coming from broadcasting rights. The fans and league custodians will surely agree that changing the social attitudes within football will change the way the game is played on the pitch or off it in the case of handbags at the Bridge, Cesc at it’s epicentre. Who was responsible for officiating that game again?

    I am quite aghast at all of the top level flair players leaving the league because they risk limb and career due to poor officiating, whilst Arsenal in particular are unable to capitalise on this trend for failing to adopt an unsporting ethos or non footballing tactical strategy in order to maximise the impact of the referee due their own creative impotency.

    I myself would be in full support of investigative action regarding referee bias, OPTA could play a particularly pivotal role in producing a dossier enclosing a complete record of actual/awarded fouls/penalties, the attacking grid reference of the correct/incorrect decision, the impact of that measure of interference in terms of direct/indirect attacking passages of play resulting in direct/indirect chance creation allowing for inferences such as the quality of chance.

    Anyone who would suggest that your piece is poorly contrived is priggish at best, although in terms of improving the Forum, I believe slurs or rather 4th principle opinions legally allowable within the confines of the Data Protection Acts 4th Principle should likely be confined to comments and remain uncensored provided no expletives are used.

    That said the PIGMOB could be the next Muppet show, Dean would be Gonzo,, East would be Animal and Moss the Fuzzy Bear, indeed their forebears should be insulted.

    All that said, City huffed and puffed and poor Pelligrini can only think back and say that choice to announce early sure cost that Pep Guardiola’s city, snigger! Meanwhile \Eriksson picked up an automatic suspension for accumulated cards, Ali cracked and stumbled, Dembele lost his cool and thank heavens because he is good at No:10. Kompany broke down (again) and City will be all at sea without their charismatic rearguard enforcer.

    with three points at City almost certainly ensuring we pick up the maximum six before our race is run, Wenger will likely ensure we qualify directly for the 20th consecutive Champions League campaign (indeed more than a trophy painful as that might be). The task now is about pride, fight, the foundations for a season, the invincible campaign began with an unbeaten run at the end of the previous season and finishing below Spurs is never an option.

    The Gunners vulnerabilities were duly exposed throughout the 15/16 campaign, the pace (or lack there of) of Per, the waning reaction times of the still re-splendid Cech, the communicative inefficiencies in Gabbys game. Even the PFA team of the years Hector was a little out of his depth more than once over the course of the season. Alexis should have sat out Chiles friendlies as advised and Ozil is yet to find the newest incarnation of the Nesut who lit up the 2006 World Cup (before Jose) a mercurial talent who not unlike Hazard may take a little while to recover from his former coach.

    Elneys arrived a window too late although only the most pessimistic of people would have predicted the two long term injury’s to two key midfielders, or anyone who believed the article above.

    Love him or hate him, but any football appreciating fool should respect Wenger. he believes in the beautiful game as do I, it’s ability to unite nations and cross borders should never compromised.

    16/17 I can only see two clubs competing, Spurs and Arsenal, with everyone else in transition, there is no time like the present to strengthen.

    Kante, Granit, Manolas, Guerreiro and Reus for me are all must buys, not if we can, not among candidates, not there is competiont, I mean must buys.

    In the must sell catagory, Giroud, he’s been exposed, he lacks the mental strength, Per, let him retire elsewhere, when a German tells you his hear isn’t in it, you should probably drop him regardless.

    and Finally Theo, highest bidder, maybe finally the little boy who won’t grow up can full fill his fathers vicarious dream and play for Liverpool, or maybe City’s need for home grown talent and a style of play suited to the speedster will see Wenger see a pragmatic solution to our commitment to FFP and a self sustaining model.

    Drafting in players before the European tournament begins will be a strategy shared across europe and although Wenger claims to ‘not be in transfer mode’ it may be suggested that a lot of work is going on behind the scenes as Arsene looks to build on foundations build from extensive scouting and previous enquires regarding player availability.

    However with Jon Toral, Chuba Akpom, Gedian Zelalem, Ashley Maitland-Niles, Isaac Hayden and Szcznesy all having exceptionally productive loan spells, the future indeed looks bright as Serge Gmabry will also be looking to put Tony ‘I hate everyone’ (great manager) Pulis behind him.

    I can only imagine that Wenger is getting better at poker as his economics background unfortunately becomes an incredibly effective tool in the modern era of football. With only 1 outfield player joining this campaign and several elder statesman due to depart, forecasts highlight a great future for the club that has been part of his life for as long as Wenger’s University of Cambridhge based daughter.

  9. I too have done some analysis on this covering the last ten years, and we are way below any of the other side, and even slightly lower than the spuds.

    I have to say though, I think one of the problems that causes this, is the lack of appealing by our side. Recently, I have seen little attempt to influence referees, compared to other sides, who seem to have it down to a tee. Perhaps referees, of which I am one on a sunday, find it easier not to give for us and consequently, because of our lack of aggression towards them, easier to give against us. That definitely has an affect when you have to make a split decision during a game.

  10. Overall, Andrew’s analysis of the officials to ref our next game, have been more than a trifle accurate over the season. Agreed that additional analysis would be great to have but at what cost…to whom?

  11. @dokat

    I said I wasn’t a statistician. All I’ve done here is present a whole rage of facts (against which there is no published contra argument). I have not tried to categorically prove anything. What I have done is taken a whole range of broad indicators which demonstrate that which ever way one looks at it, we are not getting the rub of the green.

    Having said that, your own arguments leave a little to be desired. For example, your statement that, “possession in the penalty box doesn’t necessarily lead to a penalty”, whilst slightly obvious and very true is spurious to say the least. I’d certainly argue that without possession in the box the likelihood of a penalty is much more rare.

    Also, you argue that the 0.9% difference in possession between AFC and CFC is marginal. As I said, I’m not a statistician so you may be correct. I would point out though that 0.9% difference over seven seasons actually means (by my reckoning) that AFC actually had the ball for some 35.9 hours than CFC. Just saying…….

    Similarly, to state that, “a lot of the relationships you use (e.g. a link between possession and the award of penalties) defy logic because penalties are random events” does in fact defy logic itself. Or are you really trying to tell me that a team with 10% possession is likely to have as many penalty shouts as the team that has 90% possession?!!

    In terms of your guidance telling me what I should look at, well quite frankly I spent a lunch hour looking at what I looked at. If I was a full-time academic I’d love to do what you suggest. In the meantime, I’m more than happy for you to spend time analysing over 200 penalties one by one!!! As for analysing non-penalty awards……….you are talking about almost 100,000 minutes of play to look through, I’m getting on a bit and not sure I’d actually live long enough to do that one. Maybe you’re a bit younger than me, if you start now, who knows…………

    Many thanks for the critique and suggestions. Next time can I suggest you actually contribute something rather than telling others what they should do!

    @John L

    Profound apologies, you’re quite correct and I didn’t think it through. I actually like muppets but utterly despise Riley!


    Wow! Thanks for your support mate 🙂 (and everybody else’s)

  12. norsgeneral – players shouldn’t have to appeal, the referees should do their job. I’m also glad our players don’t surround referees and try to bully them as has been known from some other teams.

    Chances are in any case, going on observation, that if our players appeared to challenge the referees, they would be carded. Mesut was carded for waving a hand dismissively after a foul was issued against him. No doubt his reaction was because the opponent had been fouling him unpunished throughout the match.

  13. Mike
    Brilliant. Thanks for the time and effort.

    Unfortunately some will still try to find one tiny detail to explain away all this. One question for these individuals, why is it that the argument will have a negative result in Arsenal’s case only, while the result will be positive and similar for all or any other top side/s you look at, whatever arguement it is that you’ll come up with, even though they all have different styles?

  14. Goonermikey – an excellent analysis thank you.

    Dokjat – The idea is to review possession time in the opponents penalty area (and vice-versa) is very good – but I just don’t think that data is available. I’m sure Opta could probably get for you for a price though? The best easily available proxy for this data, I would suggest, is the number of goals scored/conceded (as a very high proportion of goals are scored from inside the box). Indeed, for most teams, this does seem to be the case.

    However your comment that penalties are random is not valid. Penalties are like a poisson distribution. The likelihood of a penalty being awarded in, say, a given minute (or entry into the penalty box) is very low – but the number of trials is very high (particularly over 8 seasons). So, it is difficult to draw conclusions from, say, a single match. However over multiple seasons then it IS possible to draw conclusions. My contention is that the probability of the actual penalty distribution we have seen since, say, 2009 is a random fluctuation is probably significantly less than 0.01%. However my stats capabilities are rusty and I wouldn’t have time anyway to crunch the numbers. Perhaps another reader can help?

    Some posters have asserted, under previous threads, that the level of refereeing bias observed is proportional to Arsenal’s position in the League: the higher we are the more biased the refereeing. I haven’t attempted to analyse this so it would seem to be anecdotal unless someone can do the work.

    Then there are the referee reviews which document all the penalty decisions (for and against, given and not given) in Arsenal matches which offers strong evidence that we are receiving far fewer penalties than we should (and conceding more).

    The likelihood of penalties being awarded is a function of a combination of factors, including, for example: possession time in the penalty box, speed/trickiness of attacking players, clumsiness of defensive players, the ability of attacking players to simulate, the ability of defensive players to be crafty with their fouling, the ability of both sets of players (and spectators) to intimidate the referee and, of course, the bias of the referee – for whatever reason.

    The clear evidence mounts – but we all know (or should know) that it is by now incontrovertible.

  15. @ Al

    That’s exactly my point. I’m not a statistician but by looking at the issue from many different angles it is possible, in my view, to identify trends. All I did was find that a number of different issues all pointed to a bias against Arsenal. Now whilst in isolation any one angle would be a pretty limp argument, my amateur take on this was that if you look at enough issues and all or most of them point to the same conclusion then that would suggest that there’s a reasonable likelihood that this conclusion is true. Not rocket science……………..but then I don’t want to get into that argument again 🙂

  16. Goonermikey — I agree my comment can be construed to suggest that you conduct the analysis as I described. It was however meant to show how difficult the exercise would be, in my opinion, to yield any real conclusions regarding the award/non-award of penalties. My apologies if it came off the wrong way. I don’t think any of us have the time and resources to conduct such an exercise, including myself. Thus, my “contribution” was really to shed a different light on your analysis.

    You asked: “are you really trying to tell me that a team with 10% possession is likely to have as many penalty shouts as the team that has 90% possession?” I don’t know about shouts, but yes, it is likely for a team with 10% possession to be awarded a penalty. It’s a random event. Team A could be under pressure the whole match, with very little possession, but on a break, the opposing team B commits a foul in the penalty box to stop the break, and the referee awards a penalty to team A. Yes, I recognize the probability of this event is low, but the level of possession, or lack thereof on the part of Team A, had no bearing on the penalty they were awarded. They got a penalty because the referee was of the opinion, rightly or wrongly, that a player in team B contravened the rules of the game in relation to penalties. So to me the real exercise is an analysis of the refereeing decisions with regards to penalties, and I know it’s a challenging one.

  17. Nice work Mike – Thank you!

    It is a great shame that the major player in the Premier League (such a force in world football in so many ways) is the PIGMOB!

  18. Mike
    A lot of work went into this , I can imagine, and this is probably the only issue I’m in complete agreement with most contributors on here.

    Statistics aside, when watching referees work our games, I get the impression their mind set for giving penealties to Arsenal is to ” avoid it whenever possible” because there’s very little , or no backlash in the aftermath.

    Unless it’s a stone cold penalty( and these are very rare), most pundits will say things like; ” not for me” ,” not enough contact”, ” Have seen them given”, ” referee had a good view”, “referee didn’t have a good view”,
    or any other bs euphemism instead of the ” referee gets this one wrong” , when describing other teams penalty shouts.

    Arsene might say something along the lines ;” we probably should’ve had a penalty, I have to look at it again”, or ” We were a bit unlucky with the penalty call”, or if he’s really pissed he might just say ” special circumstances” and the whole incident gets about as much attention
    as a wrongly awarded throw in at the halfway line.

  19. I think Mike did a good job. He looked at a problem with a simple model, and then added complexity to his model in an attempt to better explain differences. And of course, he has some assumptions which influence how he looks at results.

    The most important part is in the second paragraph, “So I thought I’d check …”.

    I don’t know that people good with statistics (such as the people writing papers about football at arXiv) assume that football is 50% random , but it is a lot random. Another way to state the problem is that there are usually not enough goals scored to indicate which team is better. This statement ignores the defence component of the game. And the better statisticians have noticed that a better indicator of quality of a team is goal difference, not points accumulated. Which isn’t to say that goal difference is a good indicator of team quality.

    If we look at the laws of the game, a penalty MUST be awarded under certain circumstances. And most referees ignore that instruction (MUST). If a foul takes place in the penalty box, that would result in a direct free kick anywhere else on the field, it is to be a penalty kick (to restart play). The ball does not have to be anywhere near the event. The ball does not have to be traveling towards the event.

    How many penalties are awarded, when the ball is not within playing distance of the foul which leads to the penalty kick?

    If a team plays such that it almost never shoots at goal within the penalty box, it could easily never be awarded a penalty. If a team plays such that nearly all its attempts at goal are the result of passing such that the last touch (before the ball crosses the goal line segment) is merely a redirection (no kinetic energy added to ball), it is much more likely to be fouled in the box and hence be awarded a penalty.

  20. Mike, should be congratulated on attempting to shed a little light on the awarding of penalties.

    Of course, there are “errors” in the data selected! A small sample of 4, with 2 under-performing this season, is a “noise”.

    StatsBomb, has a former analytic employee of a football club, involved. Needless to say, Opta is the source for data.

    Mike, to his credit, was looking for a trend. Possession, is either active (in the opponent’s half). or passive (in the defender’s half).

    IMHO, shots on target, would be a better indicator?

    It is too easy to criticise, but thanks to Mike’s work, we have a comparison between 4 clubs.

  21. This is a good article. There is some merit to what Dokjat says insofar as it is possible to have sterile possession that is not seen in simple possession figures and yet the figures that Mike has used doesn’t/can’t take into account the ludicrous amount of times that we weren’t awarded penalties. As many Gooners are, I am frustrated by the seemingly endless calls that go against us. I am also curious about what are players/manager can do to change this. I ask the question whether we are branded as divers by the PGMO lot? Certainly I do not like the way Giroud reacts when he gets fouled. Should they be called? Yes but I would suggest that Olivier reacts too publicly and maybe, just maybe doesn’t get calls because of it. I dunno…Maybe we should just tell the players to absolutely refuse to go down in the box and start swinging your elbows when someone latches on. I always liked this less celebrated tool in Dennis Bergkamp’s tool box.

  22. Good article. And to think the fouls against column, contains only the fouls that the referee has chosen to see. And doesn’t include the many instances of (yellow card) tackles for which the referee waves play on.

  23. Great article Mike

    Oh what I wound not give to see the house of cards that is the PMGO fall.
    These kind of articles will keep chipping away at the bricks and more people are starting to sit up and that notice.
    It’s been so blatant this season it’s unreal.
    It’s about time the board stood up to be counted over these men who pass for refs. I know some people think that they may not want to rock the boat but when it’s this blatant how can they not do something.
    If the board has made protests and this is still going on where does that leave Arsenal? Something has to give here and I sincerely hope it’s the PMGO necks.

  24. Here’s a few thoughts I had:
    What if Arsenal players are taught to be honest?
    WHat if, due to our possession based game, other teams feel compelled to dive more often when they have a rare chance in the box?

  25. Djokat
    These stats are telling. What you’re saying is true; a team spends the entire match camped in their own box only to be fouled on a break. But that is the exception, rather than the rule. When you taking stats over a long period such as the one covered by Mike here, I don’t think you’ll find many such penalties.

    Another way to look at it is man city and Utd were more like us in terms of possession, territorial advantage etc, so their stats shouldn’t be too dissimilar from ours. Chelsea, on the other hand, might have benefitted from a penalty or two from a break, as they don’t tend to bomb forward too much like the other three. But even then you’d find they’d have more of the lion’s share of possession in more than half of their matches in the PL.

    Your suggestion is more likely to be true for a side that occupies the lower half of the table, a side such as Southampton or Villa. If such a side was included in this analysis then maybe. But in this case we’re talking of 4 teams who expect to have the majority of ball possession whenever they play in the PL, unless they’re playing against each other. So in this case, the penalty scored on a break is actually rare, and might account for something like 1% only.

  26. @Ross

    Or, are we perceived as divers and thus don’t get the calls? Our players go to ground, too. Since it is clear that we are not getting the calls we might as well tell our players to NOT go to ground and then perhaps…perhaps and we might start getting calls going our way and maybe, just maybe the neutrals will be won over. Personally, I hate seeing any player whether they wear a foreign colour or our red and white throwing themselves to the floor and then wailing at the ref.

  27. GoingGoingGooner

    My impression is that our players go down less often than those of many other teams, and that in general they try to stay on their feet and either try to score or try to pass to a team mate.

    Whether they do this because they play fairer or because they know they have no chance of being awarded a penalty, or for some other reason, I don’t know.

    But our team can’t win – I’ve seen people attack our team because they fail to go down in the penalty box!

    About Giroud – I think the criticism that he is a moaner is a bit unfair. I always remember Arsene Wenger saying that Giroud comes off the pitch having fought 100 battles. I think he is fouled constantly without any foul being awarded. A lot of these we probably don’t even notice. So I can understand his frustration. And his mild moaning is nothing to the kind of snarling that some players from other teams direct at the referee.

  28. Very impressive work Mike, and it surely proves what we already know by watching the refs time and time again wave away our clear cut calls for penalties. The players must feel so angry and let down by these awful refs. Something has to happen soon or our team will end up too demoralized.

Leave a Reply

Your email address will not be published. Required fields are marked *